Fast Erasure-and-Error Decoding and Systematic Encoding of a Class of Affine Variety Codes

In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector spaces, one corresponds to information symbols and the other is indexed by the support of Grobner basis, are canonically isomorphic, and moreover, the isomorphism is given by the extension through linear feedback shift registers from Grobner basis and discrete Fourier transforms. Next, the lemma is applied to fast unified system of encoding and decoding erasures and errors in a certain class of affine variety codes.Comment: 6 pages, 2 columns, presented at The 34th Symposium on Information Theory and Its Applications (SITA2011

Quest for the Quark-Gluon Plasma

Present status and future prospect of the quest for the quark-gluon plasma with untrarelativistic nuclear collisions are discussed.Comment: Invited talk given at Tokyo-Adelaide Joint Workshop on Quarks, Astrophysics, Space Physics, University of Tokyo, Jan.6 -10, 200

Gauge Symmetry and Neural Networks

We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and resembles lattice gauge theory of high-energy physics. Time dependence of synapses describes the process of learning. The mean field theory predicts a new phase corresponding to confinement phase, in which brain loses ablility of learning and memory.Comment: 9 pages, 7 figure